Finite Group Databasebeta

C2×#21424495 #28590248

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21424495

Splittings

SylowC59 ⋊ C2×#1887

Subgroups

subgroupG/H
centerC23#14273695
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC22×#127×C59C2
socleC23×C59#120
cosocleC22×C4×C59C24
hypercenterC22×#127D59
hypocenterC59C2×#1887
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#127

2526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 171127);